The government has refused to guarantee that foreign European Union nationals already in the UK will be allowed to remain once Britain leaves the EU, a decision condemned by Labour as causing “chaos” to huge numbers of families.

The junior Home Office minister James Brokenshire said the government could only reassure EU nationals they could remain in Britain for now, and that their status in coming years was a matter for a new prime minister.

Brokenshire, answering an urgent question from the Labour MP Gisela Stuart – herself a prominent Brexit supporter – said it would be “unwise” for the government to guarantee anything without reciprocal assurances about the status of the 1.2 million UK nationals living elsewhere in the EU.

Stuart condemned the government stance, saying it was “deeply, deeply offensive” to deny millions of people the right to plan their lives for the next couple of years. “People are not bargaining chips,” she said.

Andy Burnham, the shadow home secretary, was more outspoken still, saying the non-British EU nationals in the country, who had arrived in the expectation they could stay permanently, were having the “rug pulled from under them”.

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“The 3 million or so EU nationals living here are the fathers and mothers, aunties and uncles, grandmas and grandads of millions of British children,” Burnham said. “Any uncertainty hanging over their right to be here is tantamount to undermining family life in our country.”

The government, in refusing to act, was “creating the conditions for the unwelcoming climate to continue and the rises in xenophobic and racist abuse we have seen rising in recent days”, Burnham added.

Launching her leadership bid, she said: “I commit today guaranteeing rights of EU friends who have already come here to live and work. We must give them certainty, there is no way they will be bargaining chips in our negotiations.”

Stuart had tabled the question to seek reassurances about the legal status of foreign EU nationals once Brexit happens, in the light of comments by Theresa May. The home secretary, and frontrunner to replace David Cameron as prime minister, had on Sunday refused to offer any guarantees, saying negotiations with the EU “will need to look at this question”.

To groans from some MPs, Brokenshire said he could only say there would be “no immediate change” to the status.

“The prime minister has been clear that decisions on issues relating to the UK’s exit from the EU will be for a new prime minister,” Brokenshire said. “I’m therefore not in a position to make new policy announcement this afternoon.”

The only way to decide the matter would be as part of reciprocal negotiations with other EU countries about British nationals living elsewhere in the bloc, Brokenshire said, rather than offering unilateral guarantees.

“This would be unwise without a parallel assurance from European governments regarding British nationals living in their countries,” he said. “Such a step might also have the unintended consequence of prompting EU immigration to the UK.”

Burnham told Brokenshire he had a personal interest in the matter, as his wife was Dutch and their three children were half Dutch.

He condemned May’s comment on Sunday that “nobody necessarily stays anywhere forever”, calling this “quite threatening”. Burnham told Brokenshire: “I hope the minister will go back and tell the home secretary that my own kids would quite like their mum to stay here forever, if that is OK with her.”

Burnham was also highly critical of May for not being in the Commons personally. A lack of planning over such issues had “reduced our country to chaos, and created uncertainty being felt in every family”, he said.

He added: “If the home secretary wants to be the person to lead us out of it, she needs to have the courage to come to this house and clear up her own mess.”

May’s stance found almost no support among her fellow Conservative MPs in the Commons, with those criticising the position including Bill Cash, Sarah Wollaston and Crispin Blunt. The other four Tory leadership candidates have all said EU nationals already in Britain should be allowed to stay.